Alexander Barnaveli Georgia Magnet II III IV V I A sequence of identical steel balls includes a...
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Transcript of Alexander Barnaveli Georgia Magnet II III IV V I A sequence of identical steel balls includes a...
Alexander Barnaveli
Georgia
Magnet
IIIII
IVV
I
A sequence of identical steel balls includes a strong magnet and lies in a nonmagnetic channel. Another steel ball is rolled towards them and collides with the end ball. The ball at the opposite end of the sequence is ejected at a surprisingly high velocity. Optimize the magnet's position for the greatest effect.
1. Gaussian Cannon
Presentation Plan
1. Experiment
2. Gaussian Cannon action principles
3. Interaction of magnet and ball
4. “Energy source”
5. Gaussian Cannon optimization
6. Multi-stage Cannon
Experiment
VideoSlow motion shot
Potential (magnetic) energy: (1)
Ball velocity: (2)
Momentum conservation law Potential (magnetic) energy difference of initial and final conditions
Gaussian Cannon action principles
IIIIII
Initial and final conditions
Magnet and Ball – Magnetic Dipoles
Magnetic field picture
Force measurement
Our installation Schematic representation
(z – Distance between centers, Magnet dipole moment: )
Acting ForceInteraction force of magnetic dipoles:
Magnetic dipole creates magnetic field in vacuum equal to [1]:
Due to magnetic field, magnetic dipoles are induced in balls [1]:
μ- magnetic permeability of steel
Thus the interaction force of magnet and ball is:
Magnetic Field VisualizationSingle Magnet in Free Space
Grade = N52Diameter = 0.5inThickness = 0.5in
Magnet length: 2a
Dipole moment of magnet:
Experimental Magnets
Steel ball radius: a=0,64 cm Mass: m=8 g Magnetic permeability of steel: μ = 700 » 1 Magnet length: 2a Dipole moment of magnet:
• Magnetic dipole creates magnetic field in vacuum equal to [1]:
(3)
• Due to magnetic field, magnetic dipoles are induced in balls [1]:
(4)
• Dipole energy in magnetic field: (5)
III
Energy – Initial Condition Magnet
Center of the 1st ball: z=2a Center of the 2nd ball: z=4a Magnetic moment induced in ith ball :
• Magnetic moments in centers of 1st and 2nd balls are:
• Magnetic field in centers of 1st and 2nd balls :
• - Magnetic field in the center of ith ball• Using (5),(7),(8) - Magnetic energy of initial condition is:
III
(6)
(7)
• Using (6) and (7) - magnetic moments induced in balls are:
(8)
(5)
Energy – Initial Condition Magnet
Magnetic field in centers of 1st and 2nd balls:
Induced magnetic moments in balls:
Using (5), (10) and (11) potential (magnetic) energy of final condition is:
III
Energy – Final Condition Magnet
Potential (magnetic) energy difference of initial and final conditions:
The velocity is calculated using kinetic energy:
In our experiments:
For single-stage 1+2 balls case:
Theoretical estimation of velocity
Experimental calculation of velocity
Video (3-7)
Different number of balls for 1 section
Different number of balls for 1 section
Maximal velocity is achieved with 1+4 balls
Reasons:Energy loss (heat, rotation)Alignment of balls Comparison of Pipe and Rails
Vmax
Multi-sectional installation
ShotSlow motion shot
Velocity for “n” sections
Fixing the magnet to avoid it’s backward movement
Alignment of balls strictly along one line
In case of multi-stage cannon alignment of magnet poles
Using same-size balls and magnet
Consideration of using non-magnetic balls behind the magnet
Consideration of different masses of the last ball
Important Points of construction
We constructed the Gaussian cannon
Energy source of cannon - difference of the initial and the final potential energies
Interaction of magnet and ball = interaction of magnetic dipoles
Optimal configuration of cannon: One ball before magnet, other balls (2 or more) - behind the magnet
We calculated the ball velocity for 1+2 ball variant of cannon. Theoretical calculations coincide with experimental results.
In one-stage cannon maximal velocity is achieved for 1+4 ball configuration.
We considered some features of multi-stage cannon
The very important points of the construction are:
Fixing magnet to avoid it’s backward movement Alignment of balls strictly along one line Using same-size balls and magnet
Conclusion
Thank you for attention!
References:
1. Kirk T. McDonald. A Magnetic Linear Accelerator. Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544. (March 3, 2003)
2. Christian Ucke, Hans Joachim Schlichting. Die Magnetkanone. Phys. Unserer Zeit. 3/2009 (40). P. 152
3. http://en.wikipedia.org/wiki/Force_between_magnets
4. http://en.wikipedia.org/wiki/Dipole ; http://en.wikipedia.org/wiki/Magnetic_dipole